A closed form formula to predict the ultimate capacity of pitted mild steel plate under biaxial compression

The aim of the present paper is to investigate the effects of pitting corrosion on the ultimate capacity of mild steel rectangular plates under biaxial compression, extending earlier results of uniaxially loaded plates. A series of non-linear FEM analysis of plates with partial depth corrosion pits are carried out, changing geometrical attributes of both pits and plates, i.e., the radius, depth and location of pits and the slenderness of plates. Simulation results show that volume loss dominates the degradation of the compressive capacity of pitted mild steel plates as well as loading ratio. Plate slenderness has considerable effect on biaxial interaction curve shape. A regression analysis of FEM results is conducted leading to a closed form formula able to predict the remaining strength of pitting corroded plates, where both volume loss and plate slenderness are taken into account. The proposed formula will facilitate a quick estimation of the remaining strength of pitting corroded plates during lifetime ship design phase which is relevant to maintenance decision-making of aging ship structures and components.     

Ultimate strength of I-girders under eccentric patch loading: Derivation of a new strength reduction coefficient

In structural applications I-girders are subjected to eccentric patch loading since even a small eccentricity of applied loads relative to the web plane is unavoidable in practice. Experimental research shows that the behaviour of eccentrically loaded girders differs from that of concentrically loaded girders. A reduction in ultimate strength due to eccentricity is evident, and some expressions for the reduction have been proposed. We show that these expressions overestimate the reduction in capacity for large eccentricities. In this paper, results of 102 tests on I-girders subjected to eccentric patch loading are presented and the variables involved in the phenomenon are evaluated based on a parametric study of experimental data and the results of several finite element models. The parametric study confirms that the parameters previously identified for evaluating the effect of small eccentricities are sufficient for addressing cases with larger eccentricities. New mathematical expressions are proposed herein to represent the reduction in strength across the full range of eccentricities considered.     

Spatial time-dependent reliability analysis of corroding pretensioned prestressed concrete bridge girders

Accelerated pitting corrosion tests have been performed to obtain spatial and temporal maximum pit-depth data for prestressing wires. This data is then used to develop probabilistic models of pitting corrosion and strength capacity of 7-wire strands. The probabilistic model of pitting corrosion for strands is then combined with a non-linear Finite Element Analysis and probabilistic models of corrosion initiation and propagation to study the spatial and temporal effects of pitting corrosion on a typical pretensioned prestressed concrete bridge girder. The limit states considered are flexural strength and serviceability. The spatial time-dependent reliability analysis takes into account the uncertainties and variabilities related to material properties, dimensions, loads and corrosion parameters as well as the spatial variability of pitting corrosion of prestressing strands. Including the spatial variability of pitting corrosion in the reliability analysis increased both the probability of strength and serviceability failure when compared with a mid-span sectional analysis.     

Ultimate strength of cracked plate elements under axial compression or tension

In addition to corrosion, fatigue cracking is another important factor of age related structural degradation, which has been a primary source of costly repair work of aging steel structures. Cracking damage has been found in welded joints and local areas of stress concentrations such as at the weld intersections of longitudinals, frames and girders. Fatigue cracking has usually been dealt with as a matter under cyclic loading, but it is also important for residual strength assessment under monotonic extreme loading, because fatigue cracking reduces the ultimate strength significantly under certain circumstances.In this paper, an experimental and numerical study on the ultimate strength of cracked steel plate elements subjected to axial compressive or tensile loads is carried out. The ultimate strength reduction characteristics of plate elements due to cracking damage are investigated with varying size and location of the cracking damage, both experimentally and numerically. Ultimate strength tests on cracked steel plates under axial tension and cracked box type steel structure models under axial compression are undertaken. A series of ANSYS nonlinear finite element analyses for cracked plate elements are performed. Based on the experimental and numerical results obtained from the present study, theoretical models for predicting the ultimate strength of cracked plate elements under axial compression or tension are developed. The results of the experiments and numerical computations obtained are documented. The insights developed will be very useful for the ultimate limit state based risk or reliability assessment of aging steel plated structures with cracking damage.     

波浪腹板工形梁局部承压承载力设计方法研究

波浪腹板工形梁的局部承压性能目前国内外研究较少。在总结前人对平腹板和梯形波折腹板梁局部承压极限承载力研究工作的基础上,对波浪腹板工形梁的局部承压性能及设计方法进行研究。通过有限元数值分析,揭示波浪腹板工形梁在局部压力作用下的破坏形式以及腹板几何初始缺陷对局部承压性能的影响,在几何参数分析的基础上建立局部承压极限承载力的简化计算公式。最后针对同时承受局部荷载和弯矩的波浪腹板工形梁,建立截面弯矩与局部压力之间的M-P承载力相关计算公式,并通过有限元数值计算进行验证。     

双翼缘荷载作用下腹板开洞冷弯型钢截面的腹板压屈(1):试验和有限元分析

进行了82个腹板压屈试验,其中20个试验为没有开洞腹板的槽形截面,62个为有开洞腹板的槽形截面。试验考虑了端部双翼缘受荷和内部双翼缘受荷2种工况。在有开洞腹板的试验中,洞口直接位于集中荷载处。集中荷载通过承重板施加;研究了不同支承长度的影响。另外,还考虑了翼缘与支撑固定和不固定2种工况。介绍了非线性弹塑性有限元模型,研究表明,在强度和失效模式下有限元模拟结果与试验结果均吻合较好。     

Shear buckling in foam-filled web core sandwich panels using a Pasternak foundation model

Web core panels, foam-filled sandwich panels with interior webs, are a structurally efficient option for transverse load bearing applications. In web core panels, the interaction between the webs and core material can have a substantial impact on web shear buckling strength and is a key element of lightweight structural design. The present work is an investigation of web buckling behavior in web core panels under a distributed load. To solve this problem, web shear buckling was analyzed for the case of pure shear loading with foam support, and this analytic model was extended to the case of panels with a transverse distributed load. The webs are modeled as simply supported plates resting on a Pasternak elastic foundation. To that end, a buckling model for plates on a Pasternak foundation is presented, along with closed-form approximations of the solution for square and infinitely long plates. An accurate model for the foundation constants is developed using energy methods. Applicability of the plate buckling model to web core panels with transverse loads is presented via a finite element study. In panels, the slenderness and spacing of the webs have a slight effect on the boundary conditions between the webs and face sheets. The effect is relatively small, however, and the model presented in this work underpredicts buckling strength by less than 25%. The model in this work is thus a reasonable approach to the practical design of web core panels.     

A design rule for web crippling of cold-formed steel lipped channel beams based on nonlinear FEA

This paper presents the details of a research study conducted with the aim of developing an alternative design rule to predict the web crippling strength of cold-formed steel lipped channel beams. Current empirical web crippling design rules are perceived to be only accurate for the type of sections and the section dimensions that have been tested. A large number of experiments are often necessary to validate these design rules for a wider range of section types and dimensions, and these experiments are often expensive and impractical. Hence, a design rule which is based on a theoretical or numerical model has been attempted through this work.Four series of tests, replicating the four web crippling loading conditions namely: Interior-One-Flange (IOF), Interior-Two-Flange (ITF), End-One-Flange (EOF) and End-Two-Flange (ETF), were performed to predict the ultimate strength of one hundred and eight specimens. The test specimens were manufactured to include three distinct corner radii and two different web heights, and the specimens were tested using three different lengths of load bearing plates. Two additional loading scenarios which could arise due to the loading flange restraint namely—fixed-flange and free-flange were also examined. Finite element models were developed to numerically simulate the tests performed in the experimental investigations. Load-deformation curves were obtained from both the tests and FE models, and the FE models were validated using the test results. The validation showed a close agreement of FE results with the test results which provided the confidence of using the FE model for a parametric study beyond the limits of the experiments. Based on the results of the parametric study, a design rule was developed which is much more flexible to adapt for new types of sections and ranges of dimensions.     

Bending behavior of concrete-encased composite I-girder with corrugated steel web

A partially encased composite I-girder with flat or corrugated web has been proposed to improve the structural performance of continuous composite girder under hogging moment. The flexural behavior of such structure under two points symmetric loading has been experimentally and analytically investigated. Static flexural loading tests showed that the partially encased girder improved bending strength in comparison to steel I-girder, as local bucking of steel flange was restricted by encased concrete. Especially for the corrugated web girder, the ultimate bending strength was improved about 20%, and the ductility also increased about 3 times. In addition, the limitation of width-to-thickness ratios for steel and concrete-encased composite I-girders with corrugated web were suggested to prevent premature failure due to local buckling of compressive flange. Moreover, the analytical methods of flexural strength under service and ultimate state for partially encased composite girder were proposed and verified with experimental results. It was found that the analytical bending strengths agreed well with the experimental ones at both service and ultimate state, which means the proposed analytical equations can be applied in predicting flexural strength accurately for such encased composite girder with flat or corrugated web.     

Seismic performance of the Accordion-Web RBS connection

A new type of Reduced Beam Section (RBS) connection, “Accordion Web RBS (AW-RBS)”, is presented in this research. RBS connections are commonly known as connections with reduced flange width within a limited area near the column face. However, the AW-RBS decreases the web contribution in moment strength and a reduced section is developed in the beam. In an AW-RBS, the flat web is replaced by corrugated plates (L-shape folded plates, used here) at the expected location of the beam’s plastic hinge. While the corrugated web has adequate shear strength, its provided moment strength and flexural stiffness are negligible. Two relatively identical specimens including AW-RBS connections have been tested under cyclic loading. Both specimens provide at least 8% story drift, without any significant strength loss, which is more than current requirements for qualifying connections in special moment frames. The accordion effect of the corrugated web and the cyclic performance of the connection are verified by analytical results. According to the analytical and experimental results, the inelastic rotations of the connection are mostly provided by reliable and ductile rotation at the reduced region rather than in the connection plates or panel zone.     

Spatial variability of pitting corrosion and its influence on structural fragility and reliability of RC beams in flexure

A stochastic process for assessing the effect of spatial variability of pitting corrosion on structural reliability and fragility is developed for singly reinforced simply supported reinforced concrete (RC) beams in flexure. A distribution of pitting corrosion is inferred from existing literature. The RC beam is discretised into a series of elements and maximum pit depths are generated for each reinforcing steel bar in each element. The analysis considered various member spans, loading ratios, bar diameters and number of bars in a given cross-section. Comparisons made with general corrosion showed that pitting corrosion is more critical for smaller diameter reinforcing steel bars. It was also found that up to a three-fold increase in 50-year probabilities of failure were observed if spatial variability of pitting corrosion are included in the analysis when compared to probabilities of failure based on the mid-span limit states only. This strongly suggests that the inclusion of spatial variability of pitting corrosion can lead to significant decreases in structural reliability for flexural RC members.     

变形钢筋与混凝土黏结性能研究综述

从黏结试验方法、黏结强度和黏结应力-滑移本构关系三个方面，对单调及重复荷载作用下钢筋混凝土黏结性能相关研究进行了综述。对于中心拔出试验，钢筋与混凝土的黏结受力状态与实际工程结构有偏差，而梁式或梁端式黏结试验是相对较为理想的黏结试验方法。单调荷载作用下，对于非锈蚀钢筋混凝土，黏结强度以及黏结应力-滑移本构关系的研究均较为完善，成果已在各国或地区规范中体现；对于锈蚀钢筋混凝土，黏结强度劣化规律的研究已有大量数据积累，并已建立了以钢筋锈蚀率或锈胀裂缝宽度为变量的黏结强度劣化模型，但单调荷载作用下锈蚀钢筋混凝土黏结应力-滑移本构关系模型有待进一步完善。重复加载作用下钢筋混凝土黏结滑移性能的研究相对较少。已有研究结果表明：无论钢筋是否锈蚀，重复加载对黏结强度都没有显著影响，但是会导致钢筋和混凝土之间产生残余滑移，随加载次数和应力水平增大呈不断累积增长的趋势。根据目前研究现状，对于劈裂破坏模式下的黏结应力-滑移本构模型、腐蚀电流密度对黏结强度劣化规律的影响，基于表面锈胀裂缝宽度的黏结强度劣化模型、锈蚀钢筋与混凝土在单调及重复荷载作用下的黏结应力-滑移本构模型等，有待进一步研究。     

Inspection and maintenance planning of underground pipelines under the combined effect of active corrosion and residual stress

In this paper, a maintenance policy is proposed for pipelines subjected to active corrosion and residual stress, by taking into account imperfect inspection results. The degradation of the pipeline is induced by uniform corrosion, leading to losses of the pipe wall thickness. Localized corrosion is not considered herein, as neither pitting nor crevice corrosion are strongly influenced by external loading conditions and, hence, are not critical in structural strength considerations. When the corroded layers are removed, strain relaxation occurs, causing a redistribution of residual stresses. In parallel, the inspection is applied to detect the corrosion defects, namely the thickness of the corroded layer, and it has a detection threshold under which no corrosion rate can be measured. Due to uncertainties, each inspection is affected by the probability of detecting small defects and the probability of wrong assessment in terms of defect existence and size. The present work aims at integrating imperfect inspection results in the cost model for corroded pipelines, where the failure probabilities are computed by reliability methods. A numerical application on a gas pipe shows the influence of corrosion rates and residual stresses on the optimal maintenance planning.     

Patch loading resistance of girders with corrugated webs

The corrugated steel plate is a widely used structural element in many fields of application because of its favourable properties and has been applied since the 1920s. For the last 20 years it has been increasingly used in the web of steel and composite bridges. When such a bridge is incrementally launched, buckling of the thin steel web may occur. In this paper, a numerical model is developed on the basis of previous experiments. Numerical investigations are made for the determination of the patch loading resistance, and the geometric parameters which influence the patch loading resistance and the structural behaviour are determined and analysed. Existing design formulas from the literature are summarised from the point of view of bridges, and enhanced according to the numerical results and the existing and additional experiments.     

Web crippling behaviour of laterally restrained cold-formed steel re-entrant profiled deckings

Web crippling failure is often found to be critical in cold-formed steel profiled deckings during construction of composite slabs. Therefore, accurate prediction to the web crippling resistances of profiled deckings over internal supports under hogging moment is highly desirable. This paper presents an extensive experimental investigation into the structural behaviour of laterally restrained re-entrant profiled deckings under concentrated loads. A total of 104 web crippling tests on fully supported re-entrant profiled deckings with nominal yield strengths at 235 and 550 N/mm² are carried out to provide data for direct comparison with design resistances obtained from codified design rules. It should be noted that in the past, little attention has been paid to establish the lateral restraint condition of profiled deckings under concentrated loads in tests. Hence, local section distortion or ‘section spreading’ is often observed in tests but seldom dealt with rigorously during design development. In the present study, effective lateral restraints are provided to the test specimens in order to fully mobilize the web crippling resistances of the profiled deckings. It is found that the measured web crippling resistances are typically 20%–40% higher than those obtained from the codified design rules given in BS5950: Part 6, Eurocode 3: Part 1.3 and the North America Specification, depending on the steel grades and thicknesses, the load bearing lengths as well as the loading conditions.

In general, both BS5950 and Eurocode 3 give conservative web crippling resistances for re-entrant profiled deckings with both low and high strength steel under internal and end loading conditions. Moreover, the corresponding resistance factors determined according to a codified reliability analysis are considerably larger than the required values. Thus, the design rules are reliable and conservative, although they tend to be very conservative for profiled deckings under end loading condition. However, an examination on the design rules given in the NAS shows that only some of them are applicable to predict the web crippling resistances of low and high strength steel re-entrant profiled steel deckings. The design rule for IOF condition always gives both conservative and reliable resistances for both low and high strength steel profiled deckings, compared to the measured values. The design rule for EOF condition is also found to be both conservative and reliable for low strength steel profiled deckings only, but not for high strength steel profiled deckings. The design rules for ITF and ETF conditions are not applicable for both low and high strength steel profiled deckings according to the reliability analyses.

It is demonstrated that a set of new design rules specifically for re-entrant profiled deckings is needed for both improved efficiency and reliability. Moreover, the comprehensive set of test data is readily adopted to calibrate both finite element models and design expressions in subsequent studies.     

Experimental and Numerical Study on Buckling Behavior of a Rigidly Stiffened Plate with Tee Ribs

In the bridge structures, stiffened plates are usually designed as rigidly stiffened when the orthotropic steel box girder is used as the main load-bearing structure. Therefore, the buckling mode of stiffened plates is plate buckling which occurs in subpanel supported by stiffeners. The orthotropic steel box girder is used as the main girder for Egongyan Rail Special Bridge, which is a self-anchored suspension bridge. Plates of the steel girder are rigidly stiffened with unequal spacing open ribs, and the most slender stiffened plate is the mid web stiffened with Tee ribs. In order to ensure the safety of the bridge, the buckling behavior of the web and orthotropic steel box girder under axial compression, including ultimate strength, post-buckling behavior and failure modes, should be clearly investigated by experimental and numerical methods. The design, loading and testing methods of the 1:4 scale model of the orthotropic steel box girder are introduced in detail firstly. The orthotropic steel box girder and the stiffened web finite element (FE) models are validated by the test results, and the effects of residual stress and the magnitude of geometric imperfections are discussed roughly. Based on the validated web FE model, a detailed parametric study is performed to systematically investigate the effects of residual stress and geometric imperfections on buckling behavior of the web. The effect of shapes of geometric imperfections discussed is highlighted. Through tracing stress states, the failure modes of stiffened plate are in agreement with the experimental phenomenon to some extent. Results show that shapes of geometric imperfections have significantly influenced post-buckling behavior and failure modes of the web, but slightly affected the ultimate strength. It is advised that residual stress and geometric imperfections should be controlled to make full use of excellent performance of steel materials.     

Eccentrically patch-loaded steel I-girders: The influence of patch load length on the ultimate strength

The ultimate strength of steel I-girders is reduced when the loads are applied at an eccentricity relative to the center of the section, compared with the centric case, for which the loads are applied in the plane of the web. Current expressions for the strength reduction coefficient for eccentrically patch-loaded steel I-girders do not account for the length of the patch loading. In this paper, the effect of patch load length is investigated using a substantially larger data set than was available in the past. The length of the patch load is found to have a significant influence on the strength reduction coefficient for small ratios of flange thickness to web thickness, t_f/t_w.     

双翼缘荷载作用下腹板开洞冷弯型钢截面的腹板压屈(2):参数研究和设计公式

采用有限元法对开洞腹板压屈冷弯型钢截面进行参数研究,在内部双翼缘(ITF)受荷和端部双翼缘(ETF)受荷工况下,验证腹板开洞和截面尺寸对承受腹板压屈的槽形截面腹板的压屈强度的影响。在这2种荷载工况下,开洞位于承重板下方中部。研究证实,影响腹板压屈强度的主要因素是开孔深度与腹板厚度的比值及承重板长度与腹板厚度的比值。与试验及有限元结果相比,该文以腹板压屈强度折减系数的形式给出的设计建议较保守。     

Probabilistic deterioration model of high-strength steel wires and its application to bridge cables

Bridge inspections reveal that severe corrosion and fatigue are the main failure mechanisms of bridge stay cables. This paper presents an empirical modelling of the long-term deterioration process of steel wires in cables with consideration of the simultaneous occurrence of uniform corrosion, pitting corrosion and fatigue induced by a combined action of environmental aggression and cyclic loading. Accelerated corrosion experiments are conducted to determine the different corrosion levels of high-strength steel wires, and time-dependent statistical models are developed to quantify uniform and pitting corrosion depth. Corrosion-fatigue process of steel wires is subsequently simulated using the corrosion models and cyclic stress obtained through cable force monitoring data. The mechanical properties of corroded steel wires, including yield stress, ultimate stress, ultimate strain and modulus of elasticity, are experimentally characterised, and the statistical models are established through regression analysis. Finally, the deterioration models of high-strength steel wires (including crack depth, ratio of broken wires, and remaining strength, among others) is extended to probabilistically assess the time-variant conditions of bridge cables (sectional area loss and remaining capacity). The presented study on the long-term deterioration of bridge cables would provide guidance to future decision-making regarding the maintenance and replacement of bridge cables.     

Deteriorating beam finite element for nonlinear analysis of concrete structures under corrosion

A three-dimensional reinforced concrete (RC) deteriorating beam finite element for nonlinear analysis of concrete structures under corrosion is presented in this study. The finite element formulation accounts for both material and geometrical nonlinearity. Damage modelling considers uniform and pitting corrosion and includes the reduction of cross-sectional area of corroded bars, the reduction of ductility of reinforcing steel and the deterioration of concrete strength due to splitting cracks, delamination and spalling of the concrete cover. The beam finite element is validated with reference to the results of experimental tests carried out on RC beams with corroded reinforcement. The application potentialities of the proposed formulation are shown through the finite element analysis of a statically indeterminate RC beam and a three-dimensional RC arch bridge under different damage scenarios and corrosion penetration levels. The results indicate that the design for durability of concrete structures exposed to corrosion needs to rely on structural analysis methods capable to account for the global effects of local damage phenomena on the overall system performance.